Mathematical Sciences: Foundations and Applications of Bayesian Inference and Decision Theory

本项目涉及贝叶斯非参数程序，该程序包含有关抽样分布的均值和尾部行为的信息。利用贝叶斯随机化理论，可以将有限总体扩展到非随机样本。对于存在协变量的审查数据的扩展也应该遵循。贝叶斯统计推断理论的基础问题围绕着将过去的信息或先前的意见与新的信息或数据结合起来，然后提出合并的观点。将主观观点与观测信息相结合，对于贝叶斯推理的应用以及有效的基于统计的预测和决策具有重要意义。本研究考察了基本的数学问题及其在具体科学问题中的应用。

This project addresses Bayesian nonparametric procedures which incorporate information about the mean and about the tail behavior of the sampling distribution. Extensions to non-random samples from finite populations may be developed, drawing on a Bayesian theory of randomization. Extensions for censored data in the presence of covariates should also follow. Foundational issues for Bayesian theory of statistical inference revolve around assembling past information or prior opinion with new information or data and then presenting the amalgamated view. The inclusion of subjective views with information from observations has important implications for the applications of Bayesian inference and for effective statistically-based prediction and decisions. This research examines both fundamental mathematical issues and their applications to specific scientific questions.